Dispersion in tubular reactors

We now compare the solution of the hyperbolic model with that of the parabolic model used widely in the literature to describe dispersion in tubular reactors. The parabolic model with Danckwerts boundary conditions (in dimensionless form) is given by... 

In Chapter 8, axial dispersion in tubular reactors was discussed. Typical industrial reactors have sufficiently high flow rates and reactor lengths so the effects of axial dispersion are minimal and can be neglected. A rule of thumb is that axial dispersion can be neglected if ... 

The dispersion in tubular reactors depends on the flow regime and is characterized by the Bodenstein number, the ratio of the axial diffusion time, tu,ax, in the reactor to the mean fluid residence time, x. 

For the design of tubular reactors an a priori estimation of the axial dispersion is indispensable. The dispersion in tubular reactors depends on the flow regime, characterized by the Reynolds number. Re, and the physical properties of the fluid, characterized by the Schmidt number. Sc. In addition, the presence of internal packings influences the flow behavior and, in consequence, the axial dispersion of the fluid. 

Table 3.2 Estimation of axial dispersion in tubular reactors [6].

Figure 3.15 Axial dispersion in tubular reactors (a) laminar flow and (b) turbulent flow. Gray area represents experimental results. (Adapted from [6], Figure 27.25 Copyright 2012, Wiley-VCH GmbH Co. KGaA.)...

The dispersion in tubular reactors can be estimated for stratified flow in microchannels by introducing Equation 3.73 in the o-number. 

Initiators. The degree of polymerization is controlled by the addition rate of initiator(s). Initiators (qv) are chosen primarily on the basis of half-life, the time required for one-half of the initiator to decay at a specified temperature. In general, initiators of longer half-Hves are chosen as the desired reaction temperature increases they must be well dispersed in the reactor prior to the time any substantial reaction takes place. When choosing an initiator, several factors must be considered. For the autoclave reactor, these factors include the time permitted for completion of reaction in each zone, how well the reactor is stirred, the desired reaction temperature, initiator solubiUty in the carrier, and the cost of initiator in terms of active oxygen content. For the tubular reactors, an additional factor to take into account is the position of the peak temperature along the length of the tube (9). 

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

Note that setting one of the terms on the left side of the equation equal to zero yields either the batch reactor equation or the steady-state PFTR equation. However, in general we must solve the partial differential equation because the concentration is a function of both position and time in the reactor. We will consider transients in tubular reactors in more detail in Chapter 8 in connection with the effects of axial dispersion in altering the perfect plug-flow approximation. 

In stirred tanks, the power input to agitate the tank will depend on the physical properties of the liquid. In tubular reactors, the axial dispersion in empty tubes may be estimated [e.g., Wen in Petho and Noble (eds.), Residence Time Distribution Theory in Chemical Engineering, Verlag Chemie, 1982] as... 

An axially-dispersed, adiabatic tubular reactor can be described by the following mass and energy balances that are in dimensionless form (the reader should verify that these descriptions are correct) ... 

Gas-phase reacdotis are carried out primarily in tubular reactors where the flow is generally turbulent. By assuming that there is no dispersion and ttiere are no radial gradients in either temperature, velocity, or concentration, we can model the flow in the reactor as plug-flow. Laminar reactors are discussed in Chapter 13 and dispersion effects in Chapter 14. The differential form of the design equation... 

The axial dispersion in the reactor is often expressed by the axial Peclet number, and the characteristic length, which equals the tube diameter for tubular reactors, and the particle diameter for packed-bed reactors. The Bodenstein number characterizing dispersion in the tubular reactor thus becomes the following ... 

There are two sections on the FEMLAB ECRE CD. The first one is Heat effects in tubular reactors." and the second section is Tubular reactors with dispersion." In the first section, the four examples focus on the effects of radial velocity profile and external cooling on the performances of isothermal and noni.soihermal tubular reactors. In the second section, two examples examine the di,spersion effects in a tubular reactor. 

Evaluate the results obtained in problems 8 and 14, Chapter 4, in terms of the criterion developed by Meats for freedom from axial dispersion effects in tubular reactors [D.E. Meats, Ind. Eng. Chem. Proc. Design Devel., 10, 541 (1971)]. 

The RTD in chemical reactors is a crucial parameter for process performances and product yield and selectivity. The RTD in tubular reactors can be described by the so-called dispersion model [7]. This model suggests that the RTD can be considered as the result of piston flow with the superposition of axial dispersion. The dispersion is considered by means of an effective axial dispersion coefficient... 

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